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lfunc_lfunctions • Show schema
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{'Lhash': '1755731346226133671581946851899', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5, 2.598076211353316], 'a4': [1.0, -1.7320508075688772], 'a5': [-0.5, -0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-3.0, -5.196152422706632], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.303936668947014, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-0.5, 0.8660254037844386]]]], 'bad_primes': [7, 11], 'central_character': '539.67', 'coefficient_field': 'CDF', 'conductor': 539, 'conductor_radical': 77, 'conjugate': '1061839476277184497133078443657', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.0, 1.7320508075688772]], [[1.0, 0], [1.5, -2.598076211353316], [-1.5, -2.598076211353316]], [[1.0, 0], [0.5, 0.8660254037844386], [-2.5, 4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-4.0, 0], [13.0, 0]], [[1.0, 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03503124374891900694335864642', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.303936668947014, 'bad_primes': [7, 11], 'central_character': '7.4', 'conductor': 539, 'conductor_radical': 77, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/539/2/e/c/67/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-539-7.4-c1-0-17', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-539-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0745931333509744, 'root_angle': 0.04034590610789225, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38502781910885349746250986438', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1755731346226133671581946851899', 'Lhash_array': ['1755731346226133671581946851899'], 'label': '2-539-7.4-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/539/2/e/c/67/1'}